Managing Security Group for Shared Calendar access

I am sharing an Office 365 Calendar using a Security Group. When the calendar was initially shared, it sent invitation emails to the group members. How do I manage invitations when I add someone to the group? It doesn't appear to do it automatically.

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If an invitation is not sent, will the user realize the calendar is available for view or must he open the calendar by name? We tried just adding someone to the group and there was not indication to the user that the calendar was available. Maybe I am missing something ....